Date: Friday, February 14, 2020

Time: 2:30 – 3:30 p.m. (coffee & refreshments starting at 3:00 p.m.)

Place: HP 4351 (Macphail Room), School of Mathematics & Statistics, Carleton University

Speaker: Nils Bruin, Simon Fraser University

Title: Arithmetic aspects of Prym varieties of low dimension

Abstract: Prym varieties arose classically in the study of integration of algebraic functions as surprising relations allowing the computation of some integrals in terms of much simpler ones. In modern language, we understand this in terms of isogenies on Jacobian varieties of algebraic curves. Their most prominent modern applications arise from the fact that generally, a Prym variety is not itself a Jacobian variety of an algebraic curve, which makes them a fertile source of counterexamples.

However, for low-dimensional Prym varieties, various beautiful geometric coincidences force them to be Jacobians anyway. I will give a gentle introduction into Jacobian varieties and Prym varieties, and describe some of these coincidences. Time permitting, I will also discuss why these coincidences are advantageous for computational arithmetic geometric applications.